Is it safe to declare a mutex at file-scope?

I realize this question is similar, but mine is not specific to Windows.

Is is safe and good form to declare a mutex at file-scope like so?

#include <iostream>
#include <mutex>
#include "Logger.h"

mutex my_mutex;

void Logger::log()
{
    lock_guard<mutex> lock(my_mutex);
    for (int i = 0; i < 29; ++i)
    {
        cout << i << " ";
    }
    cout << endl;
}

I want to synchronize at instance-level, not across instances. I tested it and it worked fine. Are there any gotchas?